Small volume provers are used extensively in the petroleum industry as a means to prove custody transfer meters-meters that account the volume of product delivered from one party to another. (See the American Petroleum Institute (API) Manual of Petroleum Measurement Standards, Chapter 4, Section 3 for a description of the design of small volume provers.) The proving process confirms or modifies the meter calibration through the application of a meter factor. It is carried out as follows:                Flow through the meter to be calibrated is also directed through the prover. The flow causes a piston or similar device within the prover to pass between two position detector switches. The product volume measured by the meter to be calibrated during the period between detector switch actuations is compared against the volume of the prover between the detector switches. (Prior to using the prover, the volume between detectors is measured using a standard volume container traceable in the US to NIST. In other countries the standard volume is traceable to other national standard laboratories.) The ratio of the prover volume to the uncorrected volume measured by the meter is the meter factor. Each such meter factor determination is referred to as a “proving run”. Typically multiple proving runs are performed, and a meter factor for future operations is determined from the average of the individual prove measurements. The accuracy of the meter factor determination is enhanced by the use of multiple prove runs.        
Proving transit time ultrasonic meters with small volume provers presents a problem that is inherent in the application of the technology to the measurement of fluid flow over a period of short duration. In order to understand this problem, it is useful first to describe, as an example, the operation of ultrasonic meters.
Transit time ultrasonic meters determine fluid velocity by measuring the transit times of pulses of ultrasonic energy traveling along clearly defined paths, with and against the direction of the flow. Ultrasonic meters used for custody transfer typically employ multiple paths, sometimes in a chordal arrangement, so that the multiple velocity measurements can be combined according to an appropriate algorithm to determine volumetric flow rate. A flow rate measurement is thus performed using a set of transit time measurements. In the majority of petroleum product flow measurements, the flow is turbulent, which means that local fluid velocities vary spatially and temporally about some average. As a result a single flow rate measurement, comprised of a set of chordal measurements, will not, in general, represent the true average flow rate present at that time, but may vary over a range of about ±2%. If many flow rate measurements are made, it will be found that they form a normal distribution, centered on the average flow rate and having a standard deviation of about 1%. The uncertainty of the mean of a normally distributed population of measurements is equal to the standard deviation of the distribution divided by the square root of the number of sample measurements taken from the population. The average of multiple measurements can therefore yield an accurate measure of the average flow rate prevailing during the time over which the measurements are made.
The contained volume of a small volume prover is, as the name implies, small; consequently the duration of a prove—the elapsed time between actuations of the first and second detector switches—is short, typically between k and 1 second. The rate at which transit time ultrasonic flowmeters sample the flow rate varies among manufacturers, but is usually between 5 and 100 Hz. Using a sample rate of 25 Hz as an example, the number of flow rate samples obtained during a 1 second prove will be 25. If, as described in the preceding paragraph, the individual sample measurements obtained during the prove vary randomly about the mean, in a normal distribution with a standard deviation of 1%, the uncertainty in the mean meter factor obtained during the prove is 1%/(25)1/2=±0.2% (one standard deviation). Put another way, the meter factors determined from repeated proves will be randomly distributed about the true mean in a distribution having a standard deviation of 0.2%. API standards for custody transfer require that the meter factor be determined with an accuracy of ±0.027% at a 95% confidence level, which is equivalent to two standard deviations. Application of statistical analyses shows that over 200 prover runs would be required to determine a meter factor with the requisite accuracy.
Coriolis and vortex shedding meters, as well as other meters whose instantaneous outputs fluctuate about the true flow are subject to similar constraints. Like ultrasonic meters, these meters create a pulse train representative of volume artificially, via a variable frequency oscillator whose frequency is set by the measured flow rate.
These discussions illustrate an important difference between the meters listed in the paragraph above and flow measurement devices traditionally used in the petroleum industry. As described above, ultrasonic flowmeters compute volumetric flow rate from a finite sample of velocities measured along acoustic paths whereas traditionally used instruments, specifically turbine meters and positive displacement meters, respond continuously to the flow field as a whole—the determination of volumetric flow is inherent in their principles of operation. Turbine meters and positive displacement meters are therefore less sensitive to turbulent variations and can usually be proved in a relatively small number of prover runs, even with a small volume prover.
Despite this advantage, turbine meters and positive displacement meters are gradually being replaced by ultrasonic meters because the maintenance costs of the latter meters, which have no moving parts, are far lower. Extensive testing by the API and others, using large provers and master meters, has demonstrated that transit time ultrasonic meters are capable of delivering an accuracy of ±0.027% in petroleum applications. There is therefore a significant incentive to find a way whereby they can be calibrated effectively with small volume provers.
To address the proving shortcomings of ultrasonic meters, designers have turned to filtering of the raw flow rate samples, processing multiple samples to form a “smoothed” flow rate measurement. Similar measures have been taken by designers of coriolis meters. In most instances, the signal processing amounts to a single time constant low pass filter. With ultrasonic meters time constants as short as 0.1 seconds or as long as 10 seconds may be employed. This practice has the effect of extending the proving period (because more prove samples are incorporated in the determination of flow during the prove). It has however a significant weakness: If the actual flow rate changes just before or during a proving run, the meter factor determined from the proving data will be biased by an amount dependent on the sign and magnitude of the flow change. (The subject of errors due to sample delays as well as smoothing time constants has been explored by an API Task Group. See “Proving Liquid Meters with Microprocessor Based Pulse Outputs”, K. D. Elliot, North Sea Workshop, October, 2005, incorporated by reference herein.) The meter factor bias (which must be viewed as an error since it will not be detected) is shown as a function of the filter time constant in FIG. 1 for both step and ramp changes during a 1 second prove.
Some discussion of FIG. 1 is warranted. First, it should be noted that flow rate can and usually does change during a prove. The change is sometimes caused by the hydraulic resistance inserted by the prover itself in the flow circuit—in this case the bias produced by the flow change will be systematic and will not be removed by repeated proves. The API recognizes that flow changes can be a problem; changes can introduce errors in turbine meters as well as ultrasonic meters. Consequently, a 5% flow change during a prove is a generally accepted limit. Interpreting FIG. 1 on this basis: If a step change of 5% took place at the beginning of the prove of an ultrasonic meter having a 5 second time constant, the meter factor determined from the data of that prove would be in error by 0.9×5%=4.5%. This error is obviously far in excess of the ±0.027% allowable uncertainty in the meter factor (and the allowable uncertainty must also accommodate the prover uncertainty and the statistical variations in measured meter factor due to turbulence).
Even with shorter meter time constants the bias is significant. Suppose for example a meter employs a smoothing time constant of 0.1 seconds. FIG. 1 indicates that a step change of 5% during a 1 second prove of this meter would introduce an error of 0.1×5%=0.5%—still far outside the desired accuracy bound.
Existing Corrections to the Small Volume Proving Process
Because rotational speed of turbine and positive displacement meters is proportional to flow rate, the number of rotations produced by these meters during a proving run is a direct indication of the volume of fluid that has passed through them during the run. The rotors of these meters are equipped with a proximity detecting arrangement which produces a pulse train that allows the turns to be counted. In turbine meters the proximity devices are often affixed to each blade, so that fractions of a turn may be counted; similar measures may be taken with positive displacement meters. Despite these measures, the number of pulses produced by turbine meters and positive displacement meters during a small volume proving run may not be consistent with the precision requirement for the calibration: ±0.01%. Consequently, it is industry practice with small volume provers to employ double chronometry: a process which enhances the number of pulses measured by a fraction to achieve the requisite precision. (The principles of double chronometry are described in Chapter 5, section 6 of the API Manual of Petroleum Measurement Standards, previously cited.)
Specifically, the number of pulses measured is increased as follows:N1=Nm(T2/T1)  1)Here                N1 is the corrected number of pulses and is typically not an integer        Nm is the integer number of pulses measured during the prove by the meter to be calibrated        T2 is the time measured between the actuations of the upstream and downstream prover detection switches of the prover        T1 is the time measured from the leading edge of the first pulse produced following the actuation of the upstream detector switch of the prover to the leading edge of the first pulse following the actuation of the downstream detector switch of the prover.        
The meter factor, in volume per pulse, is then computed as the volume of the prover divided by N1.
Because their operating principles lead to a flow rate measurement (as opposed to a volume measurement), ultrasonic flowmeters, as well as other meters that may benefit from the means disclosed herein, produce a pulse train representative of the volume of product passing through them by means of a controlled oscillator whose frequency is made proportional to the measured flow rate. Although the meter designer has some control over the frequency of the pulse train, it is rarely high enough to achieve the requisite precision during a prove of ½ to 1 second duration, so that double chronometry, as described above is applied to these meters also. (It should also be noted that the use of a frequency high enough to provide the requisite resolution may not be consistent with the capability of the flow computer which receives the pulses.)
The meter factor determination and the double chronometry correction functions typically are not performed in the meter being calibrated but are carried out in a flow computer which also controls the proving process and, during normal operation, corrects meter volumetric output to standard temperature and pressure conditions.